The drying of a cellulosic fibrous material by acoustic-convective and thermal-convective methods under different conditions has been studied. Using the thermal-vacuum drying method, the weight of an absolutely dry sample of the starting material was determined and used to calculate the initial absolute and relative moisture contents, which were 12.38% and 10.96%, respectively. The dynamics of capillary impregnation and sorption wetting of samples was determined. The limiting values of the absolute and relative moisture content of cellulose fibers were found to be 862.16% and 89.47%, respectively. The kinetic curves of moisture extraction obtained in acoustic-convective and thermal-convective drying under different conditions were constructed, analyzed, and compared. It is shown that the acoustic-convective extraction of moisture has an advantage over the thermal-convective method.